相关论文: The Witten Index for 1D Supersymmetric Quantum Wal…
Split-step quantum walks are models of supersymmetric quantum walk, and thus their Witten indices can be defined. We prove that the Witten index of a split-step quantum walk coincides with the difference between the winding numbers of…
Quantum walks have attracted attention as a promising platform realizing topological phenomena and many physicists have introduced various types of indices to characterize topologically protected bound states that are robust against…
It is recently shown that a split-step quantum walk possesses a chiral symmetry, and that a certain well-defined index can be naturally assigned to it. The index is a well-defined Fredholm index if and only if the associated unitary…
We focus on index theory for chirally symmetric discrete-time quantum walks on the one-dimensional integer lattice. Such a discrete-time quantum walk model can be characterised as a pair of a unitary self-adjoint operator $\varGamma$ and a…
Recent developments in the index theory of discrete-time quantum walks allow us to assign a certain well-defined supersymmetric index to a pair of a unitary time-evolution $U$ and a $\mathbb{Z}_2$-grading operator $\varGamma$ satisfying the…
Building from work by Cedzich et al. and Suzuki et al., we consider topological and index-theoretic properties of chiral unitaries, which are an abstraction of the time evolution of a chiral-symmetric self-adjoint operator. Split-step…
It is recently shown by Asahara-Funakawa-Seki-Tanaka that existing index theory for chirally symmetric (discrete-time) quantum walks can be extended to the setting of non-unitary quantum walks. More precisely, they consider a certain…
Discrete quantum walks are periodically driven systems with discrete time evolution. In contrast to ordinary Floquet systems, no microscopic Hamiltonian exists, and the one-period time evolution is given directly by a series of unitary…
The discrete time quantum walk defined as a quantum-mechanical analogue of the discrete time random walk have recently been attracted from various and interdisciplinary fields. In this review, the weak limit theorem, that is, the asymptotic…
The continuous limit of one dimensional discrete-time quantum walks with time- and space-dependent coefficients is investigated. A given quantum walk does not generally admit a continuous limit but some families (1-jets) of quantum walks…
Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. To be analogous to the hitting time for a classical walk, the quantum hitting time must involve repeated measurements as…
Suzuki's split-step quantum walk on the one-dimensional integer lattice can be naturally viewed as a chirally symmetric quantum walk. Given the unitary time-evolution of such a chirally symmetric quantum walk, we can separately introduce…
Discrete-time quantum walk in one-dimension is studied from a path-integral perspective. This enables derivation of a closed-form expression for amplitudes corresponding to any coin-position basis of the state vector of the quantum walker…
Existence of the eigenvalues of the discrete-time quantum walks is deeply related to localization. Also, for the study of open quantum systems, non-Hermitian systems have attracted much attention. As mathematical models for such systems,…
We introduce quantum walks with a time-dependent coin, and show how they include, as a particular case, the generalized quantum walk recently studied by Wojcik et al. {[}Phys. Rev. Lett. \textbf{93}, 180601(2004){]} which exhibits…
A topological quantum number, the Witten index, characterizes supersymmetric models by probing for zero energy modes and the possibility of supersymmetry breaking. We propose an averaging method to infer the Witten index in quantum analog…
We perform the scattering analysis of the evolution operator of quantum walks with an anisotropic coin, and we prove a weak limit theorem for their asymptotic velocity. The quantum walks that we consider include one-defect models, two-phase…
One-dimensional discrete-time quantum walks show a rich spectrum of topological phases that have so far been exclusively analysed in momentum space. In this work we introduce an alternative approach to topology which is based on the…
We propose a new multi-dimensional discrete-time quantum walk (DTQW), whose continuum limit is an extended multi-dimensional Dirac equation, which can be further mapped to the Schr\"{o}dinger equation. We show in two ways that our DTQW is…
Quantum walk serves as a versatile tool for universal quantum computing and algorithmic research. However, the implementation of discrete-time quantum walks (DTQWs) with superconducting circuits is still constrained by some limitations such…